Hemispherical resonator gyroscopes are high performing vibratory rotation sensors. The hemispherical resonator gyroscope may measure rotation rates or rotation angles through rotational-vibrational coupling (e.g., Coriolis coupling) between structural modes of the gyroscope. One of the modes, designated the drive mode, is initially made to oscillate at high levels of velocity. Rotation induced Coriolis force then couples motion from the first mode into a secondary structural mode with a magnitude proportional to the magnitude of the input rotation. Commonly used vibrational modes used in hemispherical resonator gyroscopes are the two cos 2θ modes, named for their mode shape.
The ring down time is a figure of merit of hemispherical resonator gyroscopes and is commonly designated by the symbol τ. The ring down time may be considered to be the amplitude decay constant of the hemispherical resonator of the gyroscope if all external forces are removed and the hemisphere is allowed to freely oscillate. The ring down time may also quantify the amount of effort required to maintain the oscillation pattern of the hemispherical resonator, where a hemispherical resonator with a larger ring down time requires less effort. The ring down time is generally dependent on to the equivalent mass (m) and damping coefficient (b) of the hemispherical resonator where τ=2m/b.